On a Fractional SPDE Driven by Fractional Noise and a Pure Jump Lévy Noise in ℝ d

Abstract

We study a stochastic partial differential equation in the whole space $x\in {ℝ}^d$, with arbitrary dimension $d\ge 1$, driven by fractional noise and a pure jump Lévy space-time white noise. Our equation involves a fractional derivative operator. Under some suitable assumptions, we establish the existence and uniqueness of the global mild solution via fixed point principle.